Deterministic error bounds for kernel-based learning techniques under bounded noise
This work provides theoretical guarantees for kernel-based learning in robust control and system identification, but it is incremental as it builds on existing kernel methods with bounded noise assumptions.
The authors tackled the problem of reconstructing a function from noisy samples using kernel ridge regression and ε-support vector regression, establishing deterministic, finite-sample error bounds under the assumption that the true function is in the reproducing kernel Hilbert space and noise is bounded, with numerical examples provided.
We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth function belongs to the reproducing kernel Hilbert space of the chosen kernel, and the measurement noise affecting the dataset is bounded, we adopt an approximation theory viewpoint to establish \textit{deterministic}, finite-sample error bounds for the two models. Finally, we discuss their connection with Gaussian processes and two numerical examples are provided. In establishing our inequalities, we hope to help bring the fields of non-parametric kernel learning and system identification for robust control closer to each other.